NON-BINARY ERROR CORRECTION CODES 



1377 



Table XI shows that the quinary digit must be increased by 1 to 2, 

 which combined with the binary conveyed by the same decimal digit 

 yields a decimal value of 4, the original transmitted value. 



The best semi-systematic simple characteristic code for correcting 

 single small errors in a seven digit message allows 6 X 10 possible mes- 

 sages in a seven digit message (see Table V), whereas this code allows 

 6.25 X 10''. This code is therefore slightly more efficient. In addition, 

 this code has the special advantage that any error of ±2 on one digit 

 is recognizable since the corrector will have a value of 1111 for the asso- 

 ciated binary message. (An inspection of the choice of characteristics 

 and assignment of characteristics to the two components of any decimal 

 digit will confirm this.) 



This general technique can be applied to any base h channel, provided 



* If quinary information is initially generated, the combination (1, 2) will not 

 occur. 



that h is greater than 3. For odd bases, the digits which convey a parity 

 check component and an information component cannot be utilized effi- 

 ciently since one state of the base h digit is not available. For example, 

 using a base 5, (see Table XIII), only two information and two parity 

 check states may be conveyed by one digit, since the use of a third infor- 

 mation state would require at least six states for the mixed digit. In 

 the case of information digits, however, all states can be used. In the 

 ciuinary example, the resolution of a digit into two components and the 

 subseciuent recombination is subject to the restraint that one of the com- 

 binations (1, 2) will not occur, which can be assured if the information 

 source generates quinary digits. 



For the case of high redundancy codes having the property that the 

 associated binary code contains more than 50 per cent parity check 

 digits (corresponding to a negative value of n — 7n in Fig. 2), at least 

 some of the base h digits must convey two or more parity check digits. 



This can be easily accomplished: a decimal digit can convey three 



